THE nation's big-city mayors are in a bind. They are beset by growing social problems from homelessness to drugs that have already prompted many businesses and residents to escape to the suburbs. To try to resolve the problems through higher local taxes contributes little to their genuine resolution, mayors say, and only intensifies urban flight. The need to cope with growing social problems is one reason mayors of 35 of the largest cities met in New York Nov. 11-13 in a search for fresh answers.

In what was billed as the first urban summit and convened by New York Mayor David Dinkins, the mayors met behind closed doors to draft an agenda underscoring their most urgent needs and least appreciated strengths. They proposed national legislation to give tax incentives for urban investment and to free up tax-exempt bonds for broader urban uses. They also called on the movie industry to take a more-balanced look at cities.

Their hope has been to build a new sense of national responsibility for solving the most pressing urban problems. Conceding that city leaders sometimes feel defeated and overwhelmed, Chicago Mayor Richard Daley said: ``You can't isolate or separate cities from the future of this country.'' Or, as Atlanta Mayor Maynard Jackson puts it, ``If the cities don't make it, we [all] go down the tubes.''

The message of solidarity from the mayors was that they are in the market for new partners and that their dance cards are wide open. But they want more direct help from the federal government, which they feel has largely abandoned them over the last decade. ``We don't take no for an answer. ... Washington is obliged to assist us,'' insisted Mayor Dinkins.

``It's not how much more money we're going to have - it's what we do with the money we've got,'' said Rep. Charles B. Rangel (D) of New York, House deputy whip and one of the few outside speakers at the meeting. He urged the mayors both to develop more-creative proposals involving public-private partnerships - ``We're ready to help with tax incentives'' - and to make a louder and bolder effort at lobbying Congress.

Most mayors agree that to get Washington or their own states to listen, cities need to get a better handle on their own priorities. ``The list can be 25 or 30 items, but as a practical matter I think we need to refine it,'' says Walter Kenney, mayor of Richmond, Va. Most mayors say urban social ills from crime to homelessness deserve top priority.

Suburbanites rely on cities for jobs and entertainment, say the mayors. Yet most suburbs want only the barest of formal metropolitan ties. Mayor Bob Bolen of Fort Worth, Texas, stresses that a suburb without a city next door is only a town. Jerry Abramson, the mayor of Louisville, says the city should be redefined as the heart or core of a broader metropolitan community.

Some cities have tried to extract help from suburbanites through payroll taxes. New Orleans gave it a try but Louisiana courts found it unconstitutional. Suburban residents come into the city to work and freely criticize crime and street conditions, says New Orleans Mayor Sidney Barthelemy, ``but they don't want to pay a dime to help solve any of the problems.''

Each city has to look at what suburban ties, from a charge for parking privileges to a shared tax base, may be possible within that state's laws, says Kane Ditto, Mayor of Jackson, Miss. He admits that convincing suburbs of their stake in the economic health of cities will require ``a sales job.''

It is that message of interdependence and national interest in city survival that these mayors most want to convey. They stress what they have to give as centers of culture and jobs and education. They have no wish to reinforce the stereotype many have of cities as begging for handouts.